A352432 - OEIS

%I #15 Jan 14 2023 12:41:34

%S 1,1,11,29,165,593,2773,11093,48605,201829,864901,3638261,15472261,

%T 65377669,277294885,1173523013,4972873413,21056700293,89200845765,

%U 377774394309,1600161267781,6777276186821,28705824305861,121582507360709

%N Number of tilings of a 4 X n rectangle using dominoes and 2 X 2 tiles.

%C The sequence is based on A352431.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,10,-18,-14,20).

%F G.f.:(1 - 2*x - 2*x^2 + 4*x^3)/(1 - 3*x - 10*x^2 + 18*x^3 + 14*x^4 - 20*x^5).

%F a(n) = 3*a(n-1) + 10*a(n-2) - 18*a(n-3) - 14*a(n-4) + 20*a(n-5).

%e a(2)=11:

%e    ___     ___     ___     ___     ___     ___

%e   |   |   |   |   |   |   | | |   |___|   |___|

%e   |___|   |___|   |___|   |_|_|   |___|   |___|

%e   |   |   | | |   |___|   |   |   |   |   |___|

%e   |___|   |_|_|   |___|   |___|   |___|   |___|

%e .

%e        ___     ___     ___     ___     ___

%e       |___|   | | |   |___|   |___|   | | |

%e       |   |   |_|_|   | | |   |___|   |_|_|

%e       |___|   | | |   |_|_|   | | |   |___|

%e       |___|   |_|_|   |___|   |_|_|   |___|

%Y Cf. A352431, A352433.

%K nonn

%O 0,3

%A _Gerhard Kirchner_, Mar 17 2022